When thinking at welfare and government expenditure in health, we often focus on physical health and not much in mental health. Starting this project out main idea was to study the relationship between Mental Health Services and Homicides. Later, we moved to a broader view to study which are the factor that mostly impact criminality in a developed country.
After looking up for relevant data-sets on the internet, we decided to concentrate on United States of America, looking for data for each state.
The main motivation behind our project is our interest in social sciences and policies. Indeed, before starting, we decided for this topic because, possibly, our results will be interesting for a policy maker in taking decisions on education and mental health services expenditure and provision, as well as other factors.
The research questions we will try to answering throughout our project are:
Given the questions posed above, the answers we will search for in our project could lead a reader to question himself on how to exploit these presences of correlation to reach a lower level of criminality. Though, the latter consideration makes sense only if we are able to find significant relationship between the different variables.
In this part we present the data we use to analyse and answer our research questions. We start by importing and cleaning them. We use a total of 17 files to form our final data-set, we present them below separately, following the themes. Notice that we clean each data-set such that they all appear “standardized” (for example we select years from 2004 to 2013, since only in this time-framework we have all data available). This is done to facilitate the join process among all data-set.
We used the dataset on estimated crimes (from 1979 to 2019) available in the FBI website. We have repeated observations for each state in the United States of America from 1979 to 2019.
Raw data - Estimated Crimes 1979-2019 in US
The data-set contains 2116 observations for 15 variables, which are
| Missing Values | |
|---|---|
| year | 0 |
| state_abbr | 41 |
| state_name | 41 |
| population | 0 |
| violent_crime | 0 |
| homicide | 0 |
| rape_legacy | 156 |
| rape_revised | 2116 |
| robbery | 0 |
| aggravated_assault | 0 |
| property_crime | 0 |
| burglary | 0 |
| larceny | 0 |
| motor_vehicle_theft | 0 |
| caveats | 2045 |
From above we can see how many NAs we have for each feature. Looking at this we already decide to not take into account rape_revised and caveats, while we already now that state_name and state_abbr missing values refers to United States, so we will fill them appropriately.
To clean this dataset we have to transform year values into numeric. Moreover, we change the name of column state_name to State and selected only some crime which we think could be more relevant for our study and could be more impacted by mental health expenditure. We also replaced NAs in State and state_abbr with “United States” and “US”.
The cleaned dataset is called “estimated_crimes” and is reported below:
Cleaned data - Estimated Crimes 2004-2013 in US
For this part we have to download data-set for each year separately from 2004 to 2013 and you can find them at this link.
Since the structure for each year’s data-set is the same we report only the first one, for year 2004:
Raw data on Mental Health Expenditure per capita
The data-set for each year contains 51 observations for 3 variables, which are
We cleaned data-set for each year and then we joined them. To cleaned them we remove the dollar sign $ from the expenditure per capita values, as well as transform them into numeric. We also change its name of mental health expenditure per capita to the respective year of the dataset, i.e. 2004. This is done to ease the join process, which is made by State, which is the renamed previous Location.
The resulting dataset on mental health is “mh_exp” and is reported below:
Cleaned data - Mental Health Expenditure Per Capita, 2004-2013
Missing values for each feature
There are some, and if you look at data you can see that the missing value comes usually from Puerto Rico’s observation.
We used the 3 dataset in the United States Census Bureau’s website.
The first one is about race composition from 2000 to 2010Raw data - Demographics, Race, 2000-2010
This one contains 364 observations for 18 variables, which are
The second one is about age and sex composition from 2000 to 2010
Raw data - Demographics, Age & Sex, 2000-2010
This one contains 13572 observations for 19 variables, which are
The third one is about race, age and sex composition from 2010 to 2019
Raw data - Demographics, Race, Age & Sex, 2010-2019
This one contains 236844 observations for 21 variables, which are
The cleaning is done for each data-set separately. Later we proceed to join them. In all data-set we trasform REGION into a factor and we rename the levels such that total US replaces 0, North-East (NE) replaces 1, Mid-West (MW) replaces 2, South (S) replaces 3, and West (W) replaces 4.
Also RACE and SEX will become factors with respective levels labels: (White=1, BlackAfricanAmerican=2, AmericanIndianAlaska=3, Asian=4, HawaiianPacificIslanders=5, Racegreaterthan1=6 and Total= for the dataset in years 2000-2010) and (Total=0, Male=1, Female=2).
Names of variables are also changed slightly to have them in line with other data-sets and through pivot_longer and pivot_wider we adjust the structure of the table in a standardized way.
Moreover, for AGE we created some sub-groups instead of having the complete range 0-85 years old. The age groups we create are 0-17, 18-24, 25-44, 45-64, 65-84 and 85+. We still don’t know whether age composition has an impact on criminality, but we consider important to have the subgroups 18-24 and 25-44, since in education, as we will see, these two age groups are considered.
Also race groups are different in the cleaned dataset: White, BlackAfricanAmerican, Asian and Other_race. The latter comprises all the other cathegories. We also filter for years of interest (2004-2013).
In 2011-2013 we miss the observation for United States, which instead is present between 2004-2010. Therefore, we created a dataset for it by taking the sum across states, since US’s values would be the total and we put everything together for years 2011-2013 to obtain.
We end up having two data-sets on demographics, one for the years 2004-2010 and the other from 2011 to 2013. Finally, we join these obtaining the final “demographics” dataset:
Cleaned data - Demographics in US
No missing value is present. Although, notice that in the cleaning process we have to fill some Region’s values which otherwise would be missing. But, knowing the data-set and the State, it is straightforward.
For education we decided to look up for a proxy: Bachelor’s degree incidence in the population. We found two data-sets, one for the percentage of people between 25-44 years old with a Bachelor’s Degree, for years 2005-2018, and one for the number of bachelor’s conferred in the age range 18-24 per 1000 individuals, for years 2000-2018.
The former is:
Raw data - %25-44 years old people with a Bachelor’s Degree
This one contains 53 observations for 15 variables, which are
Raw data - Per 1000 18-24 years old people conferring a Bachelor’s Degree
This one contains 53 observations for 20 variables, which are
Both data-sets are cleaned separately and then put together. The main task in both is to create a new variable year and another, respectively perc_bscholder_25_44 and perc_bscconferred_18_24, therefore resulting in longer data-sets.
Notice, that the datas we had in the second data-set referred to 1000 people and was not in percentage terms as instead is perc_bscholder_25_44, therefore, to obtain perc_bscconferred_18_24 we have to divide by 1000 and multiply by 100 the data.
Another thing which is worth mentioning is the fact that in the data-set describing %25-44 years old people with a Bachelor’s Degree, we miss observations for 2004. To adjust for it we, first, create these observations as NAs, then fill them with the value from 2005. In our opinion this shouldn’t alter our analysis, because the difference from year to year is relatively small.
Then, we join the two cleaned data-sets in “edu”:
Cleaned data - Proxies for Education level
There are no missing values in this data-set, although remember that the ones we had in edu_percholder_25_44 have been filled with 2005’s values.
The data-set on GDP can be found in the Bureau of Economic Analysis, of U.S. Department of Commerce, website.
Raw Data - Dataset which gives us info on GDP, our variable of interest
In order to clean the dataset we filter for one values of Description only, since it’s the one of interest for us: Current-dollar GDP (millions of current dollars). We delete the column which are not relevat, remaining with renamed GeoName, which is now State, and 1997 … 2019. We use “pivot_longer” to create two variables year and Current_dollar_GDP_millions increasing the length of the data-set. Of course, we also filter for years in the frame 2004-2013.
The resulting dataset is “GDP_Cleaned”:
Cleaned Data - Current-dollar GDP (millions of current dollars)
No missing values are present in “GDP_Cleaned”.
Now that we have each data-set cleaned and wrangled in a “standardized” way we can join them by State and year.
Although, simply joining them produces NAs and by looking at the data we understand that this happens because some data-set considered also Divisions and this makes appear among the States also New England, Mideast, Great Lakes, Plains, Southeast, Southwest, Rocky Mountain and Far West. We filter them out, as well as Puerto Rico. Indeed, the latter presents many missing values too.
The resulting dataset is called “project”:
Final Dataset
In this section we are going to do an explanatory data analysis by using the cleaned data described in the data part. Throughout the section, we will still need some transformation of the data to facilitate the visualization and to understand everything in a deeper way.
To present the crimes and the race in a nicer way, we decide to mutate the former in term of “per 1000 inhabitants” and the latter in percentage terms. This makes sense also because different countries have different dimensions and population size. Therefore, maintaining absolute magnitudes would probably give us a wrong perception and result. We don’t change the variables’ names, though.
As you may have seen in the section on data, we end up having many features. Although some of them might be irrelevant or redundant. To see that we use a straightforward correlation command; this can be already a step towards the selection of most important variables that we may need for our analysis later.
Figure: Correlations among variables
The main findings are:
Moving forward, having observed the correlations above, we can also look into each variable.
To do so we can look up easily at the outcome of the data-set’s summary.
For age:
| Min. | 1st Qu. | Median | Mean | 3rd Qu. | Max. | |
|---|---|---|---|---|---|---|
| Age_0_17 | 0.1676 | 0.2288 | 0.2401 | 0.2394 | 0.2495 | 0.3150 |
| Age_18_24 | 0.0829 | 0.0967 | 0.0999 | 0.1010 | 0.1032 | 0.1446 |
| Age_25_44 | 0.2308 | 0.2542 | 0.2643 | 0.2662 | 0.2761 | 0.3680 |
| Age_45_64 | 0.1144 | 0.2519 | 0.2623 | 0.2609 | 0.2714 | 0.3122 |
| Age_65_84 | 0.0589 | 0.1075 | 0.1151 | 0.1140 | 0.1214 | 0.1609 |
| Age_over85 | 0.0050 | 0.0151 | 0.0174 | 0.0177 | 0.0205 | 0.0269 |
The highest percentage of population is between 25 and 64 years old while the lowest has more than 85 years.
For race:
| Min. | 1st Qu. | Median | Mean | 3rd Qu. | Max. | |
|---|---|---|---|---|---|---|
| White | 0.2557 | 0.7373 | 0.8339 | 0.8020 | 0.8908 | 0.9654 |
| BlackAfricanAmerican | 0.0041 | 0.0326 | 0.0770 | 0.1145 | 0.1566 | 0.5812 |
| Asian | 0.0060 | 0.0138 | 0.0229 | 0.0372 | 0.0407 | 0.4083 |
| Other_race | 0.0122 | 0.0210 | 0.0273 | 0.0463 | 0.0443 | 0.3396 |
The majority of the population is white, followed by black and African-American.
For crimes:
| Min. | 1st Qu. | Median | Mean | 3rd Qu. | Max. | |
|---|---|---|---|---|---|---|
| homicide | 0.0084 | 0.0269 | 0.0454 | 0.0494 | 0.0611 | 0.3487 |
| violent_crime | 0.8655 | 2.6797 | 3.5792 | 4.0563 | 5.0244 | 15.3711 |
| rape_legacy | 0.0972 | 0.2576 | 0.3131 | 0.3271 | 0.3830 | 0.8914 |
| aggravated_assault | 0.5119 | 1.5712 | 2.2706 | 2.5683 | 3.3108 | 8.0413 |
Remember that crimes are expressed in per 1000 terms.
Homicides are the less common crime, while violent crimes and aggravated assault occur on average to 4 and 2.5 people out of 1000.
For mental health expenditure, education, population and GDP:
| Min. | 1st Qu. | Median | Mean | 3rd Qu. | Max. | |
|---|---|---|---|---|---|---|
| mh_exp_pc | 2.423e+01 | 7.144e+01 | 9.883e+01 | 1.201e+02 | 1.451e+02 | 4.099e+02 |
| perc_bscconferred_18_24 | 1.939e+00 | 4.586e+00 | 5.505e+00 | 5.661e+00 | 6.397e+00 | 1.374e+01 |
| perc_bscholder_25_44 | 1.948e+01 | 2.572e+01 | 2.987e+01 | 3.056e+01 | 3.408e+01 | 6.535e+01 |
| Current_dollar_GDP_millions | 2.266e+04 | 7.300e+04 | 1.738e+05 | 5.605e+05 | 3.818e+05 | 1.678e+07 |
| population | 5.091e+05 | 1.715e+06 | 4.352e+06 | 1.173e+07 | 7.092e+06 | 3.160e+08 |
In this last summary table, it’s worth mentioning that
To present the most important data by State we created an interactive map you can access by clicking here which shows the selected variable distribution in US’s states in a given year. Just to give you a preview of what you can see through our interactive map we report here the part of it with population values in 2004:
State’s Population in 2004 in US
Moreover, we try to analyze graphically the main variables separately in order to potentially detect outliers or interesting path/characteristics.
We start with a time series for mental health expenditure per capita, both for the whole US and the single regions. To do so we compute the median value in each region for every year and create a time series on R. Then we plot the whole thing in one graph:
We can see that in general, the expenditure per capita has increased from 2004 to 2013, with some ups and downs throughout the period. The downward sloping part are especially relevant in two regions, West and South between 2009 and 2010/11. We don’t have enough data, but a possible explanation could be the financial crisis which had impact on government budgeting. The largest difference between 2004 and 2013 values is observed for North-East, while the smallest is for South, of which gap between these years is of $7 circa. In the time series we only look at the median. It could be interesting to observe the same data through a boxplot to understand variability and outliers.
We start by looking at each regions and US in total.
We notice that US has a low variability, but here data for US are already considered as a total, it doesn’t consider each state observed. Instead, for the regions we capture, as before, that North-East is the one with largest variation, and we already know from the time series that this is due to the steadily increase in mh_exp per capita over the years.
The boxplots are ordered by median and we can see how North-East is the one with greatest median and how US’s median (which we can consider as the mean median across regions) is second for magnitude. Thus, it’s driven significantly by North East states expenditure.
South and Mid-West are the regions in which states seem to spend less for mental health expenditure in per capita terms.
We can clearly observe some outliers. But you can notice that they are quite clustered. Probably each group of outliers represents a state’s obervations in different years. These are not a problem for our analysis, therefore we just continue.
The second boxplot we propose is to shed the light on each region’s state.
As we expected, in regions such as South and West, where we observed outliers in the boxplot before, there are states which appear far from the others. These are District of Columbia and Alaska. The latter is indeed on the west coast, but it’s somehow detached from the other states of the region. Also District of Columbia is a case on its own since it’s not a proper state but a federal district.
We confirm that Mid-West is the region with less variability among its states in mental health expenditure per capita.
Let’s continue our univariate visualization part with demographics variables.
We do so by exploiting barplots. Again, we group results by regions as it can give us an idea of the distribution of population among the different US’s areas. Of course, we continue to look also at the total US. To group results by region we took median values and computed percentages of the population.
We start with a barplot for race composition of the population:
We immediately observe that between total US and North-East the difference is minimal. Although, no large difference is present for any of the region. In all of them there is a high prelevance of white people. The percentage for them is the highest in Mid-West area, while there’s a particular high percentage of Black/African-American population in the South.
Moreover, while the group “other race” is a minority everywhere, it is not in the West, where instead Black/African-American percentage is lower than both asian and other races.
Now on age composition:
The same results on overall observations throughout US as we had on the summary table in the data overview section return here. What’s new is the fact that we can make consideration on the “age” of each region. Although the composition of the population does not change in a relevant way.
Again, we group results by region and we took median values of the percentage of bachelor’s degree holder with age 25-44. We can notice from the following graph that, using our proxy for education, we have a lower percentage of bachelor’s holder in the South. Instead, North-East seem has 6% more educated people than the mean value of US.
We also look at a boxplot to understand the variability of education inside each region. The variability is not too high, although we observe some outliers in South, again we think they are due to District of Columbia:
Again, we group results by region we took median values and transform values in per 1000 terms. So, finally we ask ourselves the distribution of crimes in US.
South and West have the highest level of criminality, with a great departure from other regions for violent crimes and aggravated assaults. Violent crimes seem to be the most common crime, while homicide is the least frequent and it is the lowest in Mid-West.
Now that we discussed variables by themselves, we can start to see the various relationships that exist between multiple variables at the same time. Notice that when appropriate we use a log10 scale. This is useful for some of our variables because they cover a large range of values. We also decide to remove District of Columbia and United States, since in most cases the first creates outliners and is not a proper state and because US are just a total observation.
Since from the corrplot in the first part of the EDA section the correlation between mental health expenditure and criminality appeared dubious we start investigating this relationship through a scatterplot. We consider mental health expenditure per capita against the various kinds of criminality: homicides, violent crime, rape and aggravated assault.
From the scatterplot above we can see that the overall correlation is slightly negative. Which means that for an increase in public mental health per capita spending there is, on average, a decrease in criminality.
Remember that from the corrplot we have identified a positive correlation between education and mental health expenditure per capita. The higher the education the higher is the spending for health. We tried to show this through a scatterplot and the outcome is exaclty what we expected by the corrplot, even if we don’t rule out the District of Columbia.
This second scatterplot that we propose is criminality against education.
Here we can see two distinct things. First of all the correlation is negative, thus, on average, the higher the education the lower is the criminality rate. The second thing we can notice is about the log GDP. In all the criminalities, except rape, the lighter dots (higher GDP) lies above the tendency line, while the darker dots (lower GDP) lies below. Therefore, there is a positive correlation between GDP and the kind of crimes we considered, except for rape, that has a negative correlation.
Now we want to see a few of the correlation we saw before, but in the time dimension.
First of all the effect of mental health expenditure on criminality over time. We decided to report here the time series for only one crime, homicide, since the patterns are similar for all the four of them:
From this time series we can see how in the US the number of total homicides decreases over time. This can possibly follows from an increase in the mental health.
Now we check the mental health spending against the education over time.
Here we see that the increase in education over the selected decade also correspond to an increase in the public expenditure in mental health.
Finally we check the homicides against the education. Again, the pattern is similar also for other type of crimes, therefore we report only the one for homicides:
This final time series shows that in the decade of interest the decrease of homicides also correspond to an increase in education.
However to better understand all of these effect and draw stronger conclusions we should do some panel data analysis on the data-set as we will do in the next section.
To further study the impact of the different factor on criminality we try to exploit econometric regressions.
We start with a standard OLS for a model, where we consider total criminality per 1000 people, as the sum of rape, homicide, violent crime and aggravated assault, all in per 1000 terms. The OLS model is: \[ \begin{align*} Criminality \, per \, 1000 \, inhabitants&=\alpha+\beta_1log(GDP)+\beta_2mh\_exp\_pc+\beta_3perc\_bscholder\_25\_44+\\ & \,\,+\beta_4 White+\beta_5 BlackAfricanAmerican+\beta_6Asian + \\ & \,\, + \beta_7Age\_0\_17 + \beta_8Age\_18\_24+ \beta_9Age\_25\_44+ \\ & \,\,+\beta_{10}Age\_45\_64+ \beta_{11}Age\_65\_84+\beta_{12}log(population) \end{align*} \] Running the regression we obtain the following coefficients’ estimates:
| total_criminality | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | -146.90 | -254.92 – -38.88 | 0.008 |
|
Current_dollar_GDP_millions [log] |
4.73 | 3.52 – 5.94 | <0.001 |
| mh_exp_pc [log] | -0.30 | -0.73 – 0.12 | 0.162 |
| perc_bscholder_25_44 | -0.09 | -0.15 – -0.03 | 0.002 |
| White | -30.76 | -36.96 – -24.57 | <0.001 |
| BlackAfricanAmerican | -19.52 | -25.57 – -13.48 | <0.001 |
| Asian | -58.17 | -69.43 – -46.90 | <0.001 |
| Age_0_17 | 158.71 | 50.56 – 266.85 | 0.004 |
| Age_18_24 | 197.17 | 78.31 – 316.04 | 0.001 |
| Age_25_44 | 241.96 | 142.86 – 341.06 | <0.001 |
| Age_45_64 | 161.16 | 55.17 – 267.14 | 0.003 |
| Age_65_84 | 255.53 | 128.73 – 382.32 | <0.001 |
| population [log] | -4.20 | -5.41 – -2.98 | <0.001 |
| Observations | 505 | ||
| R2 / R2 adjusted | 0.648 / 0.639 | ||
We notice that GDP, mh_exp_pc and education’s proxy have coefficients which we could have expected by the EDA we have done previously. Indeed, GDP increases criminality while mental health expenditure and education seems to decrease it. Although, among them only \(log(GDP)\) and education are statistically significant. Surprisingly, all races have a negative effect on criminality; this doesn’t sound a convincing result since the correlation of criminality with black-african american seemed positive in the corrplot in the EDA section. By looking at the table, we see that all groups of age in percentage of the population are significant. Although, being all coefficients positive, we think there could be some mi-specification leading to biased estimators. In general, we don’t think this regression can be informative for us, since we are not considering characteristics specific to the country and the year. Indeed, using a standard OLS we ignore the fact that our data-set is a panel data.
Therefore, we tried to identify our data-frame as a panel data and to compute regression with fixed effect, random effect and first difference. Before proceeding we will explain briefly each of them:
We try to run all regression, but after some consideration we think the most appropriate for our case is fixed effect method and the reasons are:
An additional consideration we do is whether to use or not clustered standard errors. The advantage of using them would be to account for within-cluster correlation or heteroskedasticity which the fixed-effects estimator alone does not take into account. Notice that cluster-adjusted standard error take into account standard error but leave your point estimates unchanged. The results are not changing in a relevant way considering clustered-adjusted standard errors or not, though.
We would like to point out also another thought we had while running regressions. In the EDA part we have seen how Rape seems to be the only kind of crime, among the one we are considering, to behave and to be influenced differently by GDP and slightly also by the other variables. For this reason we tried to run different regressions, with as dependent variable (in per 1000 term):
In all the regressions we don’t consider Unites States since would be redundant, being a total of the other states.
We report here the results which are worth mentioning in our opinion. As said above, we select the fixed effect method. The model is: \[ \begin{align*} Y_{i,t} &=\alpha+\beta_1log(GDP)+\beta_2mh\_exp\_pc+\beta_3perc\_bscholder\_25\_44+\\ & \,\,+\beta_4 White+\beta_5 BlackAfricanAmerican+\beta_6Asian + \\ & \,\, + \beta_7Age\_0\_17 + \beta_8Age\_18\_24+ \beta_9Age\_25\_44+ \\ & \,\,+\beta_{10}Age\_45\_64+ \beta_{11}Age\_65\_84+\beta_{12}log(population) \end{align*} \] \(Y_{i,t}\) refers to the dependent variable for state \(i\) at time \(t\). The estimation is done considering \(Y_{i,t}-\bar{Y_i}\), where \(\bar{Y_i}\) is the mean dependent variable for the state \(i\). indeed \(\alpha\) will not appear in the results, as it is constant overtime.
For total criminality regression’s results are:
| total_criminality | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
|
Current_dollar_GDP_millions [log] |
3.88 | 2.74 – 5.01 | <0.001 |
| mh_exp_pc [log] | 0.16 | -0.20 – 0.51 | 0.392 |
| perc_bscholder_25_44 | -0.05 | -0.13 – 0.02 | 0.149 |
| White | -33.85 | -81.35 – 13.64 | 0.163 |
| BlackAfricanAmerican | -3.33 | -53.89 – 47.23 | 0.897 |
| Asian | -75.27 | -131.71 – -18.83 | 0.009 |
| Age_0_17 | 268.59 | 87.68 – 449.50 | 0.004 |
| Age_18_24 | 242.92 | 42.55 – 443.30 | 0.018 |
| Age_25_44 | 260.26 | 69.73 – 450.78 | 0.008 |
| Age_45_64 | 267.36 | 70.77 – 463.94 | 0.008 |
| Age_65_84 | 246.68 | 50.23 – 443.12 | 0.014 |
| population [log] | -15.85 | -20.10 – -11.59 | <0.001 |
| Observations | 505 | ||
| R2 / R2 adjusted | 0.471 / 0.397 | ||
We can notice that the \(R^2\), which is a statistical measure representing the proportion of the variance for a dependent variable that’s explained by independent variables in a regression model, is lower here with respect to the standard OLS. With respect to the standard OLS estimations, magnitudes changes but not of sign. The only exception is mental health expenditure which, here, appears having a positive effect on criminality. Although, mh_exp_pc and education’s proxy are not statistically significant anymore. Additionally, among races, only the percentage of asian in the population seems statistically significant and still negative influencing criminality. As in the OLS estimates, \(log(population)\) decreases criminality: as population increases by 1%, criminality decreases by 16 crimes per 1000 inhabitants circa.
Among the various regressions we run, only the ones with rape and homicide as dependent variables have different results from the one just presented above.
For Rape:
| rape_legacy | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
|
Current_dollar_GDP_millions [log] |
0.0762 | 0.0087 – 0.1438 | 0.027 |
| mh_exp_pc [log] | 0.0131 | -0.0081 – 0.0343 | 0.226 |
| perc_bscholder_25_44 | -0.0001 | -0.0044 – 0.0043 | 0.976 |
| White | 1.2084 | -1.6239 – 4.0407 | 0.403 |
| BlackAfricanAmerican | 1.5597 | -1.4553 – 4.5746 | 0.311 |
| Asian | -0.2739 | -3.6396 – 3.0918 | 0.873 |
| Age_0_17 | 2.8333 | -7.9549 – 13.6216 | 0.607 |
| Age_18_24 | 3.3037 | -8.6452 – 15.2527 | 0.588 |
| Age_25_44 | 5.9642 | -5.3975 – 17.3260 | 0.304 |
| Age_45_64 | 4.9356 | -6.7876 – 16.6588 | 0.410 |
| Age_65_84 | 3.1876 | -8.5273 – 14.9025 | 0.594 |
| population [log] | -0.3180 | -0.5715 – -0.0644 | 0.014 |
| Observations | 505 | ||
| R2 / R2 adjusted | 0.216 / 0.106 | ||
From the FE regression with Rape per 1000 inhabitants as dependent variable we learn that:
For Homicides:
| homicide | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
|
Current_dollar_GDP_millions [log] |
0.051 | 0.037 – 0.065 | <0.001 |
| mh_exp_pc [log] | 0.004 | -0.001 – 0.008 | 0.084 |
| perc_bscholder_25_44 | -0.001 | -0.002 – -0.000 | 0.004 |
| White | -0.061 | -0.661 – 0.539 | 0.842 |
| BlackAfricanAmerican | 1.212 | 0.574 – 1.851 | <0.001 |
| Asian | -0.820 | -1.533 – -0.107 | 0.025 |
| Age_0_17 | 2.520 | 0.235 – 4.805 | 0.031 |
| Age_18_24 | 1.483 | -1.048 – 4.014 | 0.251 |
| Age_25_44 | 0.931 | -1.475 – 3.338 | 0.448 |
| Age_45_64 | 1.394 | -1.088 – 3.877 | 0.272 |
| Age_65_84 | 2.087 | -0.394 – 4.568 | 0.100 |
| population [log] | -0.209 | -0.262 – -0.155 | <0.001 |
| Observations | 505 | ||
| R2 / R2 adjusted | 0.683 / 0.638 | ||
From the FE regression with Homicides per 1000 inhabitants as dependent variable we learn that:
The answer is inconclusive. Our study and analysis reports slightly positive correlations with crimes if we look at the Corrplot’s Figure (only exception is with Rape), but from the regression it doesn’t result statistically significant. Although, the relationship between mental health expenditure and crimes appears negative from the scatterplot and the time series we have seen in some section above.
For GDP we can say that:
For Education we can say that:
Population’s age among different states and regions does not vary significantly, therefore, through our study we can’t say much. The only thing we can extrapolate from our project regarding age-distribution comes from the corrplot. A younger population (18-44) leads to higher homicides, aggravated assaults and violent crimes. Meanwhile, older population (45+) appears negatively related with crimes. But, regressions’ output are inconclusive since estimates are all positive and with great magnitudes.
Population’s race composition could play a role. Indeed, we see that South region in US has the highest percentage of Black-African American and the highest incidence of crimes, supporting the positive correlation found on the corrplot between all kinds of crimes and Black-African American. White population is positively correlated with rape. Although from the regressions we observe that the coefficients for all races are negative when looking at total criminality. For homicides, the significant estimates for race are for black african american (1 percentage point increase in black-african american population leads to 1 homicide more in 1000 inhabitants) and asian (1 percentage point increase in asiatic population leads to 0.8 homicide less in 1000 inhabitants).
By looking at correlations and the time series reported in previous section, we would answer yes. It exists a positive relationship between the two variables, thus, the more educated the population, the higher the expenditure on mental health in the state. We can represent this findings also in the following scatterplot with the linear regression.
Up to now we could only try to guess why such a correlation exist, and which are the social factor that induce such a result.
Such opinions for the correlations are the following: